There's two ways to understand your question: as a request for example spells, or as a plea for help because you don't really know what Spirit does. There's no exhaustive list of example Spirit spells, and besides, working from a list of spells is the opposite of how the DFRPG magic system works. So I'm going to answer the latter interpretation of the question: what is Spirit? Once you've got that, then you'll be able to just make up spells and you won't need examples.
The whole point of the magic system in DFRPG is to imagine spells and then decide how to make the rules do that. To do that, you have to understand what an Element (YS p. 253) means so that you can picture the magic. If you can't together imagine what kind of magic a Spirit Evoker does, then you don't have any hope of making the magic system work. You have to start from the other side of the question: have an idea of the kind of spells and magic you want to do, then figure out whether that's Spirit or something else.
I won't cut-and-paste the copyrighted text of Spirit here, but I want to refer to it so go re-read it now. (It's page 255 of Your Story.)
First, you need to get an idea of what Spirit does. The description of Spirit talks about the sort of power it is, and has a list of things that wizards usually do with it. It's "raw" magical energy, linked to the wizard's soul and will. Its most obvious uses are creating and controlling light and creating kinetic/force effects. It's also the Element of the veil that Harry uses in the books, hiding himself and other things from the attention of others.
Second, you need to figure out what sort of spells you imagine being done with the Spirit Element. So think about that, and brainstorm some things you can do with the creation and manipulation of light and force, both blunt and subtle. (How to Brainstorm is useful here.) After brainstorming, look at the list you've brainstormed: that's a picture of what you think Spirit does. Now flip to page 293, "Example Evocation Spells", and comb through it looking for "Type: Spirit". (About half of them are Spirit Evocations.) Add those to your list. Now you've got a list of things that Spirit can do that includes both what you think it can do and what the game authors thought it could do. Mush that together, and you've got a fertile source of ideas for spells and off-the-cuff magic to make happen during play.
Now that you've got cool ideas in your head, now you can see what a Spirit Evoker does, and you're equipped for picking and choosing the magic rules you need to represent those spells.
Yes, you can cast spells without your spellbook. And yes, your list of prepared spells will stay prepared until you prepare a new list. In the Preparing and Casting spells section, only preparing a new list of spells actually requires your spellbook. Casting just requires spell slots and a prepared list of spells, and regaining spell slots just requires a long rest.
There are some other things you can't do without your spellbook, however:
- You can't cast spells as rituals.
- You can't use your Arcane Recovery feature.
- Most importantly, you probably can't learn new spells. A generous DM might rule that your two new spells learned from levelling up just appear in your spellbook, wherever it might be, but I certainly wouldn't.
- By the same token, I have no idea what would happen with the Spell Mastery and Signature Spells features if you gained them while you didn't have your spellbook. You might not gain them at all; you might gain them once you reclaimed your spellbook.
A suggestion for you: The game assumes that a Wizard has a spellbook, and a lot of the Wizard rules don't quite work without one. If you lose your spellbook, get a new one as soon as possible. For the pittance of 50 gp, you can make the rules work properly again. Even if you still don't change your list of prepared spells, it'll be worth it.
Effectively, that's it.
A wizard's spellbook serves one utility: to allow the wizard that who wrote the spellbook to prepare spells from it. This is the only inherent utility granted by the rules.
Additionally, another wizard (or multiple wizards) can copy spells from it. A generous DM might allow another wizard to study it thoroughly to decipher it to the extent that it effectively becomes their own spellbook (this is implied by my answer to your companion question on cost and is elaborated upon in this question on using another wizard's spellbook).
Otherwise, there is no utility the spellbook serves besides anything a mundane object made of paper can do. Anything else is homebrew territory for the DM.